Apparatus for evaluating functions of two independent variables



Jan 13,1931. 0, GAEDRE f 1,788,996

APPARATUS FOR EVALUATING FUNCTIONS OF TWO INDEPENDENT VARIABLES FiledJan. 29. 1929 2 Sheets-Sheet 1 lllllll ATrcRrV'E-FS.

Jan. H, 1931, v o. GAEDKE 1,788,996

APPARATUS FOR EVALUATING FUNCTIQNS OF TWO INDEPENDENT VARIABLES FiledJail. 29. 1929 2 heets-Sheet 2 INVEM'Fo/ 0770 GAE-DICE- 337 7/ 2, WMM

Patented Jan. 13, 1931 UNITED A mm OTTO GAEDKE, OI HENGELO',

ELEKTBISOHE APPABATE 1. 3. H.-, OF.

A. CORPORATION 01' GERMANY PATENT OFFICE.

mmrns Ion. nvamzlrme ruucrrons or Two murmur vazamnns Application andJanuary as, 1929, Serial No. 335,947, and in Germany December, 1927.

The invention relates to improvements in apparatus for evaluatingfunctions of two independent variables. 7

As such range-table functions there come into consideration mainly thetimeof flight of the projectile T, the timing of the fuze of theprojectile t and the elevation of the gun to, but the twist of the gun,the densit of the f f a i 1 Instead of the variables e and k may also 20be introduced the trigonometric functions of the angle under which thetarget appears, in the case of air targets, for instance, the groundangle. As well known these three values are contained in a rectangulartriantance of the object upon the horizontal plane. These variables maydirectly be determined by measurement. It is, however,

.diflicult to determine as a function of two of 80 them the time offlight of the projectile, the timing of the fuze of the projectile orthe elevation of a gun.

Although there is a possibilit of determining these values-by the aidthe rangetable, this procedure involves a reat loss of time, and israther complicate and liable to lead to reading errors. It has thereforebeen attempted to determine these functions automatically by mechanicalmeans and a kind of relief reproduction has, for instance, been employedfor this purpose. This presents, however, considerable difliculties inproduction and is very inaccurate, if it is not desired to employinconveniently large dimensions. It is also known to effect theevaluation of such functions by' graphical means, but this methodrequires much time, which is as a rule notavailable for gunnery purposesand particularly not when firlng at air targets which is formed byprojecting the dis The object of the invention is to avoid the drawbacksof the lmown apparatus. It is based upon the fact ascertained bynumerous investigations of range-tables and study of'firing results,that the functions in question may be. represented mathematically asthesum of two factors, of which the first represents a function of theone variable for the value 0 of the other variable, while the secondfactor ofthis sum forms the product of two functions of one of each ofthe two variables. The timingt of the fuze of the projectile may thus,for instance, berepresented as follows t h)=' +H -9 Correspondingmathematical expressions re- I sult for the elevation and for the timeof flight of the projectile. This-mathematical dependence may be reducedto practice by the aid of comparatively simple cam drives operatinglwith great accuracy. Accor 'ng to the invention two curve drives areemployed one of which is shaped according to a function of the onevariable for the value 0 of .the second variable, while the second curvedrive determines the'prodnet of a function of the first variable and afunction of the second variable.

In the drawings afiixed hereto and forming part of the specificationtwo'embodi- -ments of the invention are illustrated by way of example.

In the-drawings Fig. 1 shows one embodiment of the invention indiagrammatic representation,

Fig. 2 shows a graph for explaining "a simplified construction of theinvention, and Fig. 3 shows a simplified embodiment of the inventionconstructed --according to Fig. 2.

Referring to Fig. 1 of the drawings 1 is a handle, which is turned toadjust on an indicating device 2 continuously or intermittently adistance value. This adjustment is transmitted to a curve cylinder 4 bythe bevel wheels 3. The curve engraved upon the cylinder represents thedependence ac-- cording to the range-table of the timing of.

- more transmitted by the shaft 11 of the is connected with the block19.

on the parts 23 and 24 are so chosen, that.

a plain a simplified embo cylinder 4 to a threaded spindle 12 upon whicha curved body or cam member 13 is adapted to be displaced axially. Thiscurved member or cam is sha d in corre spondence with the differenttiming of the fuze in relation to the value for h=0 as function of thedistance. Turnin a handle 14 at an indication device 15 ad usts,furthermore, the elevation. The adjustment of the handle 14 istransmitted by bevel wheels 16 to a second threaded spindle 17 upon.which a curved body or cam member 18 is adapted to be displacedaxially. The curved body 18 is shaped according to the difl'erent timingvalue of the curved body 13 as a function of the elevation. Themultiplication of the values of the curved bodies 13 and 18 thussupplies the other member of the equation as differential value.

The multiplication is effected in the followin manner: Upon each curvedmember 13 an 18 is adapted to slide a block 19 and 20. Both blocks 19and 20 are displaceable .upon a rod 21 pivoted at 22 upon a fixedlymounted block. Means not shown, keep both blocks 19 and20 permanently incontact with their cam members 13 and 18..

The block 20 is free to move parallel to the shaft 11, but is preventedfrom moving at right angles to that shaft, by being made shdable on ashaft parallel to shaft 11, as shown. A rack 23 in gear with a in-ion 24he teeth the rack 23 ma move parallel to itself without rotating t ewheel 24 and that lon itudinal motion only of the rack causes t e wheel24 to revolve. The rotation of the wheel 24 is then transferred by thebevel wheels 25 to the second driving wheel 26 of the planet wheel10,-the shaft 27 of which sets itself according to the arithmetical sumof the adjustments of the two driving wheels 9 and 26.

Taking into consideration the above mathematical consideration theadjustment of the shaft 27 then correspondswith the value of the timingof the projectile, the elevation of the gun, the time of flight oftheprojectile or the value to be determined. The adjustment imparted to theshaft 27 is then transmitted to suitable instruments or to the guns.

In Fig. 2 is showna graph serving to'eximent of the invention. As anexample is assumed the determination of the elevation of the as functionof two variables. The lstance values are then plotted as abscissae andangle values as ordinates. A straight line 28 is then drawn through zeroat any an 1e, along which are marked the individua hei hts. These arethe points 29, 30 and so on. rom the end point of the distance division,which in this illustration, for instance, is marked with the numeral 100straight lines are drawn to the points 29, 30 and so on indicatingheights. Into the triangles thus formed are then traced the differencecurves, which represent the difference between the elevation accordingto the range-table for the individual heights diminished by theelevation of the gun for the heights 0 at the re- 1 spective distance.These curves are designated by the reference numerals 31, 32 and so on.Now the amount of correction for the elevation of the gun is taken intoaccount for the individual distances, which results from the particularordinate of the selected pointv on the side of one of the triangles, andthen the difference between this ordinate and the ordinate of thecorresponding point on the corresponding curve is taken into account.For instance, the difference between the ordinate of a point on'one ofthe sides of the triangle 0, 29, and the ordinate of the correspondinpoint on the curve 31 may 7 be taken. This as the advantage that thecoarse correction derived from the triangles can be formed in acomparatively simple manner, and that the difference between triangleand curve as remaining fine amount, is always comparatively small, andcan easil be obtained with great accuracy by smal curve gears.

In Fig. 3 of the drawing is illustrated an embodiment of the inventionbased on the diagram in Fig. 2. The distance value is transmitted to amember 35 provided with a curved groove through a spindle 33 and bevelwheels 34. This curve member represents in accordance with Fig.1 theelevation of the gun as function of the distance for the hei ht 0 of theobject. In this waya pin36 an rack 37 are correspondingly moved and thismotion is transmitted to a planet gear 39 across a spur and bevel gear38. The ad- 'ustment of the spindle 33 is also across vel wheels 40transmitted to a screw threaded spindle 41, upon which a slide 42 isadapted to move axially.- At right angles to the 'direction of motion ofthe slide 42 there is located a sliding rack 43. One end of the rack ispivotally connected with a slotted lever 44. The lever 44 is adapted toswing around the point 45. A block 47 adapted to slide along the spindle48 engages this slot 46. The screw spindle 48 is journaled in stationarybearings and is adjusted according to'the height of the object straightline 28' of Fig. 2, while the axis of fired at by means of bevel wheels49 and the spindle 50. By the adjustments described a coarse correctionis first eifected of the amount of motion, determined by the cylinderprovided with the curved groove.

. A comparison of Fig. 3 with Fig. 2 shows that the spindle 48corresponds with the the a scisae in Fig. 2 corresponds with the screwspindle 41 of Fig. 3. The gear of Fig. 3 containing these two parts thussupplies an amount of correction, which corresponds with the verticallines dropped from the straight line 28, Fig. 2, on the axis of theabscissae. This amount is transferred to the planet gear by a pinion 51in engagement with the rack 43, a spindle 52 and bevel wheels 53. It isnow still necessary to eflect a fine correction, which accounts for thedifference of the ordinates of the straight lines 100, 29, 100, 30 andso on of Fig. 2 in relation to the ordinates of the curves 31, 32 and soon. For this purpose there-is provided thegear 54 in Fig. 3'.'- Thiscontains a cylindrical member 55 grooved'according to the differencementioned, which is rotated by the shaft 33 across the bevel wheels 56in accordance with the distance value. On the curve member is adapted toslide one end of a rack 57, which is adapted to move longitudinally upona slide 58. The slide 58 rides upon a screw threaded spindle 59, whichby means of the bevel wheels 60. and 61 is ad usted according to thevertical distance of the target from the horizontal plane.

The slide 58 with the rack 57 isin accordance therewith displaced whenthe screw spindle 59 isturned. Since, as above described, the rack 57contacts at one end with thecurve member 55 it slides at ri ht angles.

to the direction of adjustment of t e slide 58 when this slide isadjusted.

The adjustment of the rack is across a mion 62 transmitted to a spindle63', which in its turn adjusts a planet gear 64, which is connected withthe lanet gear 39 by the .be evaluated in a corr I spindle 65. The spine 66 adjusted from e planet gear 64 then gives the desired61231118121011 of the functions, in the example c osen.

The timing of the fuze and the time of flight of the projectile asfunctions of the distance and the height of the target may din manner.Instead of distance and height tri nometrical' functions of the anglemay introduced under which the target appears, in

'. the case of airplanes the angle with the difference curves result inFig. located on the other" side of.

and plane, as already mentioned before.

f it is desired to determine the timing-of the fuze by the aid 'of thenew curve gear 2 which are the straight appertaining thereto. In such acase the curve 31, for instance, would belocated subtherefore, beelevated b tion of the target "stantially below the respective straightline ing manner, asdescribed hereinbefore with the reference to theelevation of the gun. It will be understood, that instead of the groovedcylinders illustrated in the examples other gears of equivalent functionmay be em loyed, such as spiral wheel gears.

he following example may serve to clarify the meaning of the chart shownin Fig. 2. By means of the groove cylinder 35, the shaft 66'receives amovement which represents the elevation ofthe gun for the particulardistance of the target if the target were in a horizontal plane. Thetarget, in the case of aero lanes, is at a considerable distance above te gun and the gun must, an additional amount corresponding to t e angleof elevahe angle of elevation of the target does not, however, giveexactly the correct elevation, as the raising of the firing plane ofthegun will change the necessary' elevation for a given ra e. Therefore,some correction of the ang e obtained by adding the elevation of the gunfor height zero and the elevation of the target.

must be made. Fig. 2, when considered in conjunction with Fig. 3, showshow this correction is made. 1 v

In Fig. 3, a coarse and fine adjustment are used. The abscissas in Fig.2 represents the distances, while the ordinates represent the angle. Thecurves 31, 32, 32a, 32b, 320, are curves of equal height of flight forvarying ranges or tar et distances. That is, for each height of flig tthere will be a curve representing the angle at' various ranges. ,Tlnswill supplythe correction necessary to overcome. t e inaccuracy causedby the raising of the plane of firing. For instance, in Fig.

2, for a height of flight corresponding to the curve 32a and for adistance 50, the correction would be 19. An 'arbgrlzlg straight line a28 is drawn at any d angle on which various heights 29, 30, etc., aremarked. These points are connected by straight lines with the point 100.

The screw shaft 48 co strai ht line 28, and the mem r 47 1s adjustedthereon in accordance with the height of thetarget. The screw shaft 11represents the line 0100, and the member 42 is movedproportionately tothe distance. The rotation imparted-to the shaft 52 by the turning ofthe shaft 41 represents the correcnds to the ios tion in' the angle ofelevation for a chan e m height of the target. For instance, if t edistance is 60 andthe height 30a (Fig. 2),.

'the correction would be 1, the intersection of the line 60 and the line3011-400.

However, this correction is only a coarse.

one, as it is clearfrom-Fig. 2 that the curve touched the line 60 atabout .8. It is therefore necessary to subtract from the correction of 1thecorrection of .2 for an exact result. This fine'correction is made bythe curved body 55 which is shaped .to represent the various curves 31,32, 32a, etc., and the curves therebetween. These curves run around thecylinder,- and the cylinder is rotated until the member 57 engages thatportion of the curve which corresponds to thedistance of the target. Themember 57 is moved upwards or downwards to the curve of the particularheight of'the target by the screw shaft 59 and the exact correction,both of the particular height curve and of the particular oint on thatcurve, is applied to the sha t 63 by the member 57 he curved body 55 hasan extremely irregular shape, as it is formed from the range tables andrepresents the curves of the various heights as they vary with therange.

Various modifications and changes may be made without departing from thespirit and the scope of the invention, and I desire, therefore, thatonly such limitations shall be placed thereon as are imposed by theprior 'art.

I claim as my invention: I 1. Apparatus for evaluating range table sofunctions which depend on the distance and height of the target,comprising a body having a curved oove therein, said groove representingvariations in one function according to the distance, a member adapted35 to be moved by said curved groove, a curved guide cut to representthe variations of another function with the distance, common means formoving said body and said guide by amounts proportional to the distance,a second curved uide cut to represent the variations of a hird fimctionaccording to the height, means for moving said second guide by amountsproportional to the height, a member adjustable by the combined movementof said guides and a differential device having its parts connected tosaid two members respectively, whereby the shaft of the said devlce isturned by an amount proportional to the sum of the movements of saidmembers.

2.,Apparatus for evaluating range table functions which depend on thedistance and height of the target, comprising a shaft adapted to berotated by amounts proportional to the distance, a cylinder mounted onsaid shaft having a curved groove there- 'in, said groove representingvariations in one'f unction according to the distance, a curved guidethreadedly mounted on said shaft, said guide being cut to represent thevariations'in another function according to the distance, a second shaftat an angle to said first shaft'and having screw threads thereon, asecond curvd guide mounted on said second threaded shaft, said secondguide target, apair o membersmovable in bfiin cut to represent thevariations in a t ir pivoted arm, blocks slidably mounted on said armand adapted to engage said guide'wherefunctions which depend upon thedistance and height of the target,- comprising an element movable togive the result, a bod having a curved groove therein 'correspon ing toa function of the distance for the value 0 of the height and adapted toadjust said movable element, means for moving said body in pro ortion tothe height of the roportion to the distance and height of the targetrespectively, the second of said members being moved by said body-moving means, means operated by movement of said members and operatingupon said movable element to combine the motions of said members tomultiply said motions, said last means including curvilinear meanswhereby to produce the product of a function of said distance and afunction of the height.

' OTTO GAEDKE.

function according to the height, a'

